Information on Result #2487571
Linear OOA(3192, 9847, F3, 2, 32) (dual of [(9847, 2), 19502, 33]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3190, 9846, F3, 2, 32) (dual of [(9846, 2), 19502, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3190, 19692, F3, 32) (dual of [19692, 19502, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3192, 7771, F3, 3, 32) (dual of [(7771, 3), 23121, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3192, 7771, F3, 4, 32) (dual of [(7771, 4), 30892, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3192, 7771, F3, 5, 32) (dual of [(7771, 5), 38663, 33]-NRT-code) | [i] | ||
| 4 | Digital (160, 192, 7771)-net over F3 | [i] | ||